Solve the System of Inequalities 4x+1>9 and -6x-2>10

Subtract ${\displaystyle 1}$ from both sides of the inequality.

${\displaystyle 4x>9-1}$ and ${\displaystyle -6x-2>10}$

Subtract ${\displaystyle 1}$ from ${\displaystyle 9}$.

${\displaystyle 4x>8}$ and ${\displaystyle -6x-2>10}$

Divide each term in ${\displaystyle 4x>8}$ by ${\displaystyle 4}$.

${\displaystyle \frac{4x}{4}>\frac{8}{4}}$ and ${\displaystyle -6x-2>10}$

Simplify the left side.

${\displaystyle x>\frac{8}{4}}$ and ${\displaystyle -6x-2>10}$

Simplify the right side.

${\displaystyle x>2}$ and ${\displaystyle -6x-2>10}$

Add ${\displaystyle 2}$ to both sides of the inequality.

${\displaystyle x>2}$ and ${\displaystyle -6x>10+2}$

Add ${\displaystyle 10}$ and ${\displaystyle 2}$.

${\displaystyle x>2}$ and ${\displaystyle -6x>12}$

Divide each term in ${\displaystyle -6x>12}$ by ${\displaystyle -6}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle x>2}$ and ${\displaystyle \frac{-6x}{-6}<\frac{12}{-6}}$

Simplify the left side.

${\displaystyle x>2}$ and ${\displaystyle x<\frac{12}{-6}}$

Simplify the right side.

${\displaystyle x>2}$ and ${\displaystyle x<-2}$